Question

Lauren is running for president of the student government at UTD. The proportion of voters who favor Lauren is 0.8. A simple random sample of 100 voters is taken. What are the expected value, standard deviation, and shape of the sampling distribution of proportion (, respectively?

Answer 1

`\mu_(x) = 0.8`

`\sigma  =  0.095`

The shape of this sampling distribution is approximately normal

Explanation:

From the question we are told that

The population proportion is
`p = 0.8`

The sample size is n = 100

Generally the expected value of this sampling distribution is mathematically represented as

`\mu_(x) = p = 0.8`

Generally the standard deviation of this sampling distribution is mathematically represented as

`\sigma  =  \sqrt{ (p(1- p ))/(n ) }`

=>
`\sigma  =  \sqrt{ (0.8 (1- 0.8 ))/(100 ) }`

=>
`\sigma  =  0.095`

Generally given that the sample is large (i.e n > 30 ) and the standard deviation is finite then the shape of this sampling distribution is approximately normal